41. HistoryCenter.net brahmagupta. brahmagupta was the most accomplished of the ancient Indian astronomers.His great work 'The Opening of the Universe' is written in verse form. http://www.historycenter.net/science-detail1.asp?ID=25&TimeZone=3

42. TITUS Texts: Brahmagupta, Brahmasphutasiddhanta TITUS brahmagupta, Brahmasphutasiddhanta Part No. 2 Chapter 18. at?akuakaad?yayas Verse 1a. praye?a yatas prasnas http://titus.uni-frankfurt.de/texte/etcs/ind/aind/klskt/mathemat/brsphsd/brsph00

TITUS Brahmagupta, Brahmasphutasiddhanta: Part No. 2 Chapter: 18 [atÊ°a kuá¹­á¹­aka-adÊ°yāyas] Verse: 1a prāyeṇa yatas praśnās kuṭṭākārāt rÌ¥te na śakyante / Verse: 1c j±Ätum vaká¹£yāmi tatas kuṭṭākāram saha praśnais // Verse: 2a kuá¹­á¹­aka-Ê°kÊ°a-r̥ṇa-dÊ°ana-avyakta-madÊ°ya-haraṇa-ՙeka-varṇa-bʰāvitakais / Verse: 2c ācāryas tantra-vidām j±Ätais varga-prakrÌ¥tyā ca // [kuá¹­á¹­akam] Verse: 3a adÊ°ika-agra-bʰāga-hārāt Å«na-agra-cÊ°eda-bʰājitāt śeá¹£am / Verse: 3c yat tat paraspara-hrÌ¥tam labdÊ°am adÊ°as adÊ°as prÌ¥tÊ°ak stʰāpyam // Verse: 4a śeá¹£am tatʰā iṣṭa-guṇitam yatʰā agrayos antareṇa saṃyuktam / Verse: 4c śudÊ°yati guṇakas stʰāpyas labdÊ°am ca antyāt upāntya-guṇas // Verse: 5a sva-Å«rdÊ°vas antya-yutas agra-antas hÄ«na-agra-cÊ°eda-bʰājitas śeá¹£am / Verse: 5c adÊ°ika-agra-cÊ°eda-hatam adÊ°ika-agra-yutam bÊ°avati agram // Verse: 6a cÊ°eda-vadÊ°asya ՙdvi-yugam cÊ°eda-vadÊ°as yuga-gatam ՙdvayos agram / Verse: 6c kuṭṭākāreṇa evam ՙtri-ādi-graha-yuga-gata-ānayanam // Verse: 7a bÊ°a-gaṇa-ādi-śeá¹£am agram cÊ°eda-hrÌ¥tam Ê°kÊ°am ca dina-ja-śeá¹£a-hrÌ¥tam / Verse: 7c anayos agram bÊ°a-gaṇa-ādi-dina-ja-śeá¹£a-uddÊ°rÌ¥tam dyu-gaṇas // [Cb.8]

43. TITUS Texts: Brahmagupta, Aryabhatiya TITUS brahmagupta, Aryabhatiya Part No. 2 Chapter 2. ga?itapadaVerse 1a. brahma-ku-sasi-bud?a-b?r?gu-ravi-kuja-guru-ko?a http://titus.uni-frankfurt.de/texte/etcs/ind/aind/klskt/mathemat/aryabhat/aryab0

TITUS Brahmagupta, Aryabhatiya: Part No. 2 Chapter: 2 gaṇita-pāda Verse: 1a brahma-ku-śaśi-budÊ°a-bÊ°rÌ¥gu-ravi-kuja-guru-koṇa-bÊ°a-gaṇān @namas-krÌ¥tya / Verse: 1c āryabÊ°aá¹­as tu iha @nigadati kusuma-pure abÊ°yarcitam j±Änam // Verse: 2a ՙekam ՙdaśa ca ՙśatam ca ՙsahasram ՙayuta-ՙniyute tatʰā ՙprayutam / Verse: 2c ՙkoá¹­i-ՙarbudam ca ՙvrÌ¥ndam stʰānāt stʰānam ՙdaśa-guṇam @syāt // Verse: 3a vargas sama-ՙcatur-aśras pÊ°alam ca sadr̥śa-ՙdvayasya saṃvargas / Verse: 3c sadr̥śa-ՙtraya-saṃvargas gÊ°anas tatʰā ՙdvādaśa-aśris @syāt // Verse: 4a bʰāgam @haret avargān nityam ՙdvi-guṇena varga-mÅ«lena / Verse: 4c vargāt varge śuddÊ°e labdÊ°am stʰāna-antare mÅ«lam // Verse: 5a agÊ°anāt @bÊ°ajet ՙdvitÄ«yāt ՙtri-guṇena gÊ°anasya mÅ«la-vargeṇa / Verse: 5c vargas ՙtri-pÅ«rva-guṇitas śodÊ°yas ՙpratÊ°amāt gÊ°anas ca gÊ°anāt // Verse: 6a ՙtri-bÊ°ujasya pÊ°ala-śarÄ«ram sama-Ê°dala-koá¹­Ä«-bÊ°ujā-ՙardÊ°a-saṃvargas / Verse: 6c Å«rdÊ°va-bÊ°ujā-tad-saṃvarga-ՙardÊ°am sas gÊ°anas ՙṣaá¹£-aśris iti // Verse: 7a sama-pariṇāhasya-ՙardÊ°am viá¹£kambÊ°a-ՙardÊ°a-hatam eva vrÌ¥tta-pÊ°alam / Verse: 7c tad-nija-mÅ«lena hatam gÊ°ana-gola-pÊ°alam niravaśeá¹£am // Verse: 8a āyāma-guṇe pārśve tad-yoga-hrÌ¥te sva-pāta-lekÊ°e / Verse: 8c vistara-yoga-ՙardÊ°a-guṇe j±eyam ká¹£etra-pÊ°alam āyāme // Verse: 9a sarveṣām ká¹£etrāṇām @prasādÊ°ya pārśve pÊ°alam tad-abÊ°yāsas / Verse: 9c paridÊ°es ՙṣaá¹£-bʰāga-jyā viá¹£kambÊ°a-ՙardÊ°ena sā tulyā //

44. La Formula Di Brahmagupta Translate this page La formula di brahmagupta. La formula di cui il quesito chiede di precisarela validità è nota come formula di brahmagupta (matematico http://matmedia.ing.unina.it/Concorsi a cattedra/quesiti 11 gennaio 2000/Soluzio

La formula di Brahmagupta La formula di cui il quesito chiede di precisare la validità è nota come formula di Brahmagupta (matematico indiano del VII secolo). Essa vale per i quadrilateri inscrittibili in un cerchio e quindi di un quadrilatero di lati a, b, c e d dà l'area massima. La formula è contenuta nella lista dei risultati più belli Del risultato si riporta la seguente giustificazione, chiara e immediata, tratta da d a Enciclopedia delle matematiche elementari e complementi . Segue dalle formule: le quali danno: sicché il massimo di S si ha quando è minimo cos b d , cioè per b d

45. Brahmagupta's Formula brahmagupta's Formula. For a Quadrilateral with sides of length ,, , and , the Area is given by. (1). where, (2). is the Semiperimeter http://mathworld.pdox.net/math/b/b361.htm

Brahmagupta's Formula For a Quadrilateral with sides of length , and , the Area is given by where is the Semiperimeter is the Angle between and , and is the Angle between and . For a Cyclic Quadrilateral (i.e., a Quadrilateral inscribed in a Circle , so where is the Radius of the Circumcircle . If the Quadrilateral is Inscribed in one Circle and Circumscribed on another, then the Area Formula simplifies to See also Bretschneider's Formula Heron's Formula References Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 56-60, 1967. Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 81-82, 1929. Eric W. Weisstein

46. Brahmagupta Identity brahmagupta Identity. Let. where is the brahmagupta Matrix, then, References. Suryanarayan,E. R. ``The brahmagupta Polynomials.'' Fib. Quart. 34, 3039, 1996. http://mathworld.pdox.net/math/b/b362.htm

Brahmagupta Identity Let where is the Brahmagupta Matrix , then References Suryanarayan, E. R. ``The Brahmagupta Polynomials.'' Fib. Quart. Eric W. Weisstein

47. ±Cù¼¯ÓD¦h¡]brahmagupta ¬ù598-¬ù665¡^ The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://www.edp.ust.hk/math/history/3/3_99.htm

±C¹¼¯ÓD¦h¡]Brahmagupta ¬ù598-¬ù665¡^ Nx ¡Óc=y

48. Untitled My favorite Herontype formula is brahmagupta's formula for the maximum areaof a quadrilateral KK = (s - a)(s - b)(s - c)(s - d) Does *this* have n http://www.ics.uci.edu/~eppstein/junkyard/quad-area.html

From: gls@odyssey.att.com (Col. G. L. Sicherman) Newsgroups: sci.math Subject: Re: Heron-type formulas Date: 12 Jun 90 13:03:49 GMT Organization: Jack of Clubs Precision Instruments Co. My favorite "Heron-type" formula is Brahmagupta's formula for the maximum area of a quadrilateral: KK = (s - a)(s - b)(s - c)(s - d) Does *this* have n-dimensional analogues? -:- Most people hate egotists. They remind them of themselves. I love egotists. They remind me of me. R. Smullyan Col. G. L. Sicherman gls@odyssey.att.COM

49. TITUS Texts: Brahmagupta, Brahmasphutasiddhanta Index of brsph Copyright Jost Gippert Frankfurt a/M 19992000. Noparts of this document may be republished in any form without http://titus.fkidg1.uni-frankfurt.de/texte/etcs/ind/aind/klskt/mathemat/brsphsd/

Index of brsph Jost Gippert Index of brsph Jost Gippert

50. TITUS Texts: Brahmagupta, Aryabhatiya Index of aryab Copyright Jost Gippert Frankfurt a/M 19992000. Noparts of this document may be republished in any form without http://titus.fkidg1.uni-frankfurt.de/texte/etcs/ind/aind/klskt/mathemat/aryabhat

Index of aryab Jost Gippert Index of aryab Jost Gippert

51. Kamat's Potpourri: Glossary: Brahmagupta Database). . brahmagupta. brahmagupta (598 AD660 AD) Ancient mathematicianwho worked with indeterminate equations (Varga Prakriti). See http://www.kamat.org/glossary.asp?WhoID=166

52. Índice De MATEMÁTICOS Translate this page brahmagupta se sitúa en el siglo VII, en la dinastía Gurjara, enpleno esplendor de la matemática hindú. . . . . Su vida. http://www.mundofree.com/mates/Historia/braha.htm

Su época Se sabe que en el tiempo de las construcciones de las pirámides existió una cultura muy rica en los valles del Ganges y del Indo, pero se conoce muy poco de ella, pues está escasamente documentada. Tres mil años antes de Cristo los arios invadieron y dominaron la India, imponiendo el sistema de castas que ha perdurado hasta la actualidad. Mucho después, hacia el siglo V a.C., Buda recorrió estas inmensas tierras, pero el budismo, su religión, como no respetaba este sistema social de castas, fue eliminado. Sufrieron nuevas dominaciones exteriores, pero a partir del siglo III d. C. comenzaron a reinar el país unos emperadores de origen indio, la dinastía Gupta. Dos siglo más tarde, tras la caída del imperio romano, nuevos extranjeros vuelven a ocuparla hasta el siglo XV. La última colonización, la inglesa, ha perdurado hasta hace poco tiempo. Brahmagupta se sitúa en el siglo VII, en la dinastía Gurjara, en pleno esplendor de la matemática hindú. Su vida Pocos datos se disponen de su vida. Su padre fue Jisnugupta. Nació en el año 598, posiblemente en Ujjain, donde vivió. En esta ciudad de la zona central de la India se encontraba el más famoso y antiguo observatorio de astronomía y Brahmagupta era el director. Es considerado el más grande de los matemáticos de esta época. Murió en el año 670. Su obra Su principal obra es un libro de astronomía titulado Brahmasphutasiddhanta (Sistema revisado de Brama) escrito en 628. Nos dice en esta obra que la escribió en la ciudad de Bhillamala, actualmente Bhinmal, entonces capital del país de la dinastía Gurjara.

53. Brahmagupta brahmagupta. (600660 BC). brahmagupta was born in India. Much of his personal lifeis not known to us. He did write a book called Brahma-sphuta-sidd’hanta. http://www.mvrhs.org/netsite/school/departments/Math/Jen's folder/brahmagupta.fr

Brahmagupta (600-660 B.C) He brought the concept of zero to the Western World. He introduced the principle that every positive number has two square roots, one positive and the other negative. He also thought that the quanity with zero as the denominator will have a value that is infinitely large. (kha-cheda) Bibliography Classic Math - History Topics for the Classroom Art Johnson Mathematics: A concise History and Philosophy W.S. Anglin

54. Baby Names - Brahmagupta Similar pages Elementary Geometry for College Students, 3e brahmagupta's Theorem Heron's Theorem can be treated as a corollary of anothertheorem, brahmagupta's Theorem, which can be used to calculate the area of a http://www.kabalarians.com/male/brahmagupta.htm

Kabalarian Philosophy Main Menu Home Page Important: Dear Brahmagupta: The following analysis describes a few qualities of your first name. There are many additional factors (legal name, nicknames, family surname, combined names, previous names, and business signature) that contribute to your entire personality - and your entire life. Order a Name Report for a full analysis. Brahmagupta Your name of Brahmagupta You can receive a comprehensive Name Report including all your names . It is an in-depth description of the influences affecting your personality, potential, and compatibility in personal and business relationships. Take this step to make changes in your life. Do not pass up this opportunity for a happier, healthier, and more successful future. Click here for full Name Report details Please Note: The above analysis is based on the English alphabet. Receive a FREE electronic book by giving us feedback on the accuracy of our first name analysis service, click here! Choosing a Baby Name? WARNING: Do not choose a baby name based on the short analysis given above.

55. Brahmagupta Translate this page brahmagupta. brahmagupta era il direttore dell'osservatorio astronomicoa Ujjain che era il primo centro matematico dell'antica India. http://www.geocities.com/palestra_matematica/matematici/brahmagupta.html

Brahmagupta Brahmagupta era il direttore dell'osservatorio astronomico a Ujjain che era il primo centro matematico dell'antica India. Scrisse importanti lavori di matematica ed astronomia. Scrisse " Brahma-sphuta-siddhanta " ( L'Apertura dell'Universo ), in 21 capitoli, a Bhillamala nel 628. Suo secondo lavoro di matematiche ed astronomia fu il " Khandakhadyaka " scritto nel 665. (trad. di Andrea Filieri) Torna all'indice dei Grandi Matematici e Fisici

56. Recherche : Brahmagupta Translate this page Accueil Publimath Requête brahmagupta, Certification IDDN.Dans les fiches. 5 fiches trouvées http://publimath.irem.univ-mrs.fr/cgi-bin/publimath.pl?r=Brahmagupta

57. October 26,1996 brahmagupta Polynomials in two parametersUniversity of Hong Kong Conference on Special. 3,May 1996. Properties of the brahmagupta Matrix, Int. Journal ofMath. http://hypatia.math.uri.edu/~sury/

E.R. Suryanarayan Selected Publications Pythagorean Boxes (with R.A. Beauregard), Mathematics Magazine June, 2001 S-P-2 primes (with R.A. Beauregard), The Mathematical Gazette March, 2001 Arithmetic Triangles and Bhaskara Equation (with R.A. Beauregard), College Mathematics Journal ,March, 2000. Integral Triangles (with R.A. Beauregard), Mathematics Magazine (October 2000). Brahmagupta Polynomials in two parameters University of Hong Kong Conference on Special Functions, June 21, 1999 (with Rangarajan) The Brahmagupta Polynomials in two complex variables, The Fibonacci Quarterly (Feb. 1998, p. 34-42). This paper was presented at the Seventh International Conference on the Fibonacci Numbers and their Applications held in Graz, Austria, July 1996. The Brahmagupta Triangles, (with R.A. Beauregard) College Mathematics Journal, January 1998 Parametric Representation of Primitive Pythagorean Triples (with R.A. Beauregard), The Mathematics Magazine, Vol. 169, No. 3, June 1996. Pythagorean Triples: The Hyperbolic View (Cover and Article), (with R. A. Beauregard), The College Math Journal, Vol. 27, No. 3, May 1996.

58. Hom The earliest major Indian mathematician was known as brahmagupta. ax 2 +1=y 2. brahmaguptawas also the first person to publish a sinus table for any angle. http://hypatia.math.uri.edu/~kulenm/diffeqaturi/m381f00fp/karen/karenmp.htm

Difference Equations and Recursive Relations Hindu-Arabic Period The period from 400 - 1200 signified the dark ages in the history of mathematics. Little to no major accomplishments were made in Europe, those accomplishments that were made came mainly from the middle east. During this period we begin to see the emergence of difference equations, the following is a history of those equations and the mathematicians that influenced them. The earliest major Indian mathematician was known as Brahmagupta . This mathematician introduced rules for solving simple quadratic equations of various types. He also invented a method for solving indeterminate equations of the second degree like the following: a x +1=y Brahmagupta was also the first person to publish a sinus table for any angle. Brahmagupta's matrix is given as: Powers of Brahmagupta's matrix are given as: The x n and y n are called Brahmagupta's polynomials and are given by recursive relation: x n+1 = x x n + t y y n y n+1 = x y n + y x n More information can be found in MathWorld Mathematicians , like Al-Karaji furthered the work on the algebra of polynomials to include those of infinite terms. Al-Karaji also was the first to construct

59. History 650 A.D. 650 AD In the year 650 AD the Indian mathematician brahmagupta was about 52 yearsold He wrote two books entitled Brahma sphuta- siddhanta (The Opening of the http://faculty.oxy.edu/jquinn/home/Math490/Timeline/650AD.html

650 A.D. Author : Tim Lucas References: Mac Tutor History of Mathematics Archive, http://www-history.mcs.st-and.ac.uk:/history/Mathematicians/Brahmagupta.html Brahmagupta (598-668) http://mathserv.math.sfu.ca/History_of_Math/India/7thCenturyAD/brahmagupta.html Math 490 Home Class Tasks Class Mailing List ... Timeline Last updated September 1998

60. Citation Mathematics and Computer Education archive Volume 20 , Issue 3 Fall 1986 toc brahmagupta'squadrilateral Author GS Bhalla Publisher Mathematics and Computer http://portal.acm.org/citation.cfm?id=21512&coll=portal&dl=ACM&CFID=11111111&CFT

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